Mrs May is in talks on top cabinet roles as she prepares to take over Tory leadership tomorrow
Theresa May led tributes to David Cameron at an "emotional" final cabinet meeting.
Mrs May, who posed for photographers on her way in through the door of No 10 Downing Street, and Chancellor George Osborne both marked the achievements made during Mr Cameron's six years in office.
Mrs May paid tribute to the prime minister's handling of the terror threat and said he had always put the country first.
Mr Osborne marked the introduction of gay marriage and said Mr Cameron had "left the country a better place".
Mr Cameron has chaired 215 cabinet meetings on 900 items of British government business.
Culture secretary John Whittingdale said: "It was emotional but quite rightly we spent a long time on the government business, but then we had a period during which we could raise tributes to the extraordinary service the Prime Minister has given, led on by George Osborne and Theresa May."
Small business minister Anna Soubry said Mr Cameron began by discussing how to tackle the problem of deprivation - an issue he had raised right at the beginning of his premiership.
She said she was "sad to see him go" but welcomed the arrival of Mrs May as a "safe pair of hands on the tiller".
Mrs May will become prime minister on Wednesday afternoon. First Mr Cameron will face MPs in his last Prime Ministers Questions before heading to Buckingham Palace to see the Queen.
Mrs May will then make the same journey before arriving back in Downing Street.
Mrs May, who posed for pictures as she arrived at No 10 this morning, has already begun talks with senior colleagues and allies about the top roles in her cabinet.
Her main priority is to appoint her chancellor, thought likely to be the foreign secretary Philip Hammond, in what could be a job swap with George Osborne.
She will also want to appoint a tough operator to succeed her as home secretary, with defence secretary Michael Fallon and her leadership campaign chief Chris Grayling the leading candidates.
But Mrs May will also want to give top jobs to women ministers, which could mean a promotion to the Home Office for Amber Rudd, who was a star in the TV debates during the referendum campaign.
Many MPs are predicting a return to the frontline for two Eurosceptic former ministers and Leave campaigners, Liam Fox and David Davis, who both ultimately backed her for the leadership.
These two could be candidates for the key job of Brexit minister, negotiating the UK's withdrawal from the European Union, though former leadership rival Mrs Leadsom could also be a candidate for this post.
Opposition parties are already calling for an early election - however, when she launched her campaign for the Tory leadership on June 30th, Mrs May had said: "There should be no general election until 2020."
Although Mrs May called on Gordon Brown to hold a snap election after taking over from Tony Blair in 2007, saying in he was "running scared of the people's verdict" and had "no democratic mandate".
Mr Fallon said there was no need for a snap election because the Conservatives had won the general election last year and had a mandate.
This, he said, had been reinforced by the EU referendum in which people had given the government a job to do in leaving the bloc.